On upper and lower D*-supercontinuous multifunctions

We define a multifunction F: X ⇝ Y to be upper (lower) D*-supercontinuous if F ⁺(V) (F ⁻(V)) is d*-open in X for every open set V of Y. We obtain some characterizations and several properties concerning upper (lower) D*-supercontinuous multifunctions.      

Lot-sizing with fixed charges on stocks: the convex hull

In this paper, we examine a variant of the uncapacitated lot-sizing model of Wagner–Whitin that includes fixed charges on the stocks. Such a model is natural in a production environment where stocking is a complex operation, and appears as a subproblem in more general network design problems.

Linear-programming formulations, a dynamic program, the convex hull of integer solutions and a separation algorithm are presented. All these turn out to be very natural extensions of the corresponding results of Barany et al. (Math. Programming Stud. 22 (1984) 32) for the uncapacitated lot-sizing problem. The convex hull proof is based on showing that an extended facility location formulation is tight and by projecting it onto the original space of variables.     

Second Order Nonlinear Evolution Inclusions Ⅰ： Existence and Relaxation Results

This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.     

The solution existence of general variational inclusion problems

We propose general variational inclusion problems which are slightly different from corresponding problems considered in several recent papers in the literature and show that they are advantageous. Sufficient conditions for the solution existence are established. As applications we derive consequences for several special cases of variational inclusion problems, quasioptimization problems, equilibrium problems and implicit variational inequalities and show that they improve the results of some recent existing papers.     

Preparation and Characterization of Nano-ZnFe2O4/TiO2 Films

The nano-ZnFe2O4/TiO2 films possess the functions of desulfurization and degradation for organic pollutants. The sols of ZnFe2O4/TiO2 were prepared by sol-gel method and coated on glass and porous ceramic by vertical coating and dipping-lift processes, respectively, and the samples were obtained after drying and sintering. The composition, appearance, absorption spectrum of the films, and the influence of the film on porous ceramic performances were analyzed using SEM, AFM, UV-Vis spectrometer, and mercury porosimeter, respectively, to determine the operation parameters of the multifunction porous ceramic elements for gas-purification.     

Generalised 2-circulant inequalities for the max-cut problem

The max-cut problem is a fundamental combinatorial optimisation problem, with many applications. Poljak and Turzik found some facet-defining inequalities for the associated polytope, which we call 2-circulant inequalities. We present a more general family of facet-defining inequalities, an exact separation algorithm that runs in polynomial time, and some computational results.     

Stability of multistage stochastic programming

In this paper, we study the stability of multistage stochastic programming with recourse in a way that is different from that used in studying stability of two-stage stochastic programs. Here, we transform the multistage programs into mathematical programs in the space ⁿ ×L _p with a simple objective function and multistage stochastic constraints. By investigating the continuity of the multistage multifunction defined by the multistage stochastic constraints and applying epi-convergence theory we obtain stability results for linear and linear-quadratic multistage stochastic programs.Project supported by the National Natural Science Foundation of China.     

Optimizing constrained subtrees of trees

Given a treeG = (V, E) and a weight function defined on subsets of its nodes, we consider two associated problems. The first, called the rooted subtree problem, is to find a maximum weight subtree, with a specified root, from a given set of subtrees.The second problem, called the subtree packing problem, is to find a maximum weight packing of node disjoint subtrees chosen from a given set of subtrees, where the value of each subtree may depend on its root.We show that the complexity status of both problems is related, and that the subtree packing problem is polynomial if and only if each rooted subtree problem is polynomial. In addition we show that the convex hulls of the feasible solutions to both problems are related: the convex hull of solutions to the packing problem is given by pasting together the convex hulls of the rooted subtree problems.We examine in detail the case where the set of feasible subtrees rooted at nodei consists of all subtrees with at mostk nodes. For this case we derive valid inequalities, and specify the convex hull whenk 4.Research supported in part by Nato Collaborative Research Grant CRG 900281, Science Program SC1-CT91-620 of the EEC, and contract No 26 of the programme Pôle d'attraction interuniversitaire of the Belgian government.     

Low-temperature single crystal X-ray diffraction and high-pressure Raman studies on [(CH3)2NH2]2[SbCl5]

The structure of bis(dimethylammonium) pentachloroantimonate(III), [(CH₃)₂NH₂]₂[SbCl₅], BDP, was studied at 15 K and ambient pressure by single-crystal X-ray diffraction as well as at ambient temperature and high pressures up to 4.87(5) GPa by Raman spectroscopy. BDP crystallizes in the orthorhombic Pnma space group with a=8.4069(4), b=11.7973(7), c=14.8496(7) Å, and Z=4; R₁=0.0381, wR₂=0.0764. The structure consists of distorted [SbCl₆]³⁻ octahedra forming zig-zag [{SbCl₅}_n]²ⁿ⁻ chains that are cross-linked by dimethylammonium [(CH₃)₂NH₂]⁺ cations. The organic and inorganic substructures are bound together by the N-H…Cl hydrogen bonds. The distortions of [SbCl₆]³⁻ units increase, partly due to the influence of the hydrogen bonds which became stronger, with decreasing temperature. The preliminary room temperature, high-pressure X-ray diffraction experiments suggest that BDP undergoes a first-order phase transition below ca. 0.44(5) GPa that destroys single-crystal samples. The transition is accompanied by changes in the intensities and positions of the Raman lines below 400 cm⁻¹.     

Synthesis of macrocyclic tris-cis-tris-trans- dodeca[(phenyl)(hydroxy)]cyclododecasiloxane in carbonic acid solution

The possibility to synthesize stereoregular tris-cis-tris-trans- dodeca[(phenyl)(hydroxy)]cyclododecasiloxane (tris-cis-tris-trans-[PhSi(O)OH]12) in an inorganic liquid medium – aqueous carbonic acid solution – was shown. The interaction of polyhedral phenylcoppersodiumsiloxane, {[(C₆H₅Si(O)O^?]₁₂(Cu₂⁺)₄(Na⁺)₄}*(L)_m (L?=?Buⁿ OH, H₂O), with carbonic acid can be considered as a new ‘green’ method to obtain functional organosiloxane macrocycles. In contrast to the known methods, no organic solvents were used during the reaction. The identification of the structure of the end compound was performed by means of NMR and Infrared spectroscopy as well as X-ray crystallography.